Hi Michal.
1. First, great work with detecting where the problem was, thank you for that.
2. Second, i don't think a channel manager can solve this kind of issues. If the calendar file of the provider is broken, or their service has glitches then the channel manager software will inherit the same problem. Just think about this recent outage: the channel manager queries booking.com's ics file, sees it is empty, updates airbnb accordingly by deleting all previous dates. The channel manager can't possibly know that it is a software error or you simply deleted all dates. These extreme problems however seem to be extremely rare, thankfully.
3. A much more dangerous and common situation is when the calendars sync, but not quick enough. I really have no clue how often they sync, i would have assumed that it happens at every change, where a change means a new reservation or cancelling. As far as i can see this is not how it happens, most probably because there is such a big flux of data so probably there is a prioritization or queing of data so as to not overwhelm the hardware infrastructure of the provider. Which leaves us in danger, because if the sync occurs only after a few hours there is a high chance of double booking.
So that basically leaves us with three options:
1. I am using Airbnb and Booking as well and i have grown into the habit of manually syncing the calendars after each new reservation. It only takes like 30 seconds. Especially if you have only two-three calendars to sync i think it is the best - and by far the cheapest - approach. You can instantly see if someything is wrong. And if you use aribnb/booking on a regular basis keeping an eye on these things is mandatory. There are certain things that simply can't be automated and be 100% failsafe.
2. If you are a bit technically savvy you could try to sync airbnb/booking with google calendar then write a short query using the API explorer that would interrogate the calendar on a regular basis for a certain string. Thus, if the calendar changes (for instance you had a reservation for the dates XYZ and they are not there anymore) you could get a notification and you would have to look into the problem. I used a similar, but a bit more primitive approach when this whole thing with booking.com happened that gave me enough time to react before any double bookings were made.
3. A combination of the two above is my safest bet. There is no 100% perfect failsafe system and manual check can't be completely removed.
Obviously there are many people for whom all this is science fiction because they simply are not technically inclined (well, except for the manual sync, which is really a no brainer). They are way better off using a third party software as a channel manager and that's it, BUT they must realize that bad things can happen nonetheless and that if you are trying to run a hospitality business then you must dedicate yourself to it. So yes, pick up the **bleep** phone or open the **bleep** site a few times a day even if apparently there is no reason, just to check if everything is all right. If you can do it with that piece of crap Facebook or other social network that are just for fun why don't you do it for something that actually brings you money?